Since it's a long article I will copy and paste the introduction and conclusion for the lazy brains

"Plato, acting as a kind of Socratic midwife presenting problems and puzzles in much the same way to his readers as he did in the Academy, carefully secreted a most profound Pythagorean doctrine into his written dialogues. He did so for those capable of "abducting" [1] the solution in light of the hints he provides. Here I will attempt to uncover the nature of Plato's Second Principle, known as the Indefinite Dyad, sometimes called the Greater and the Lesser, and its relation to the Golden Section, f. The crux of my hypothesis is the following:

Greater = f
Lesser = 1 / f .

This is, to my knowledge, a novel hypothesis, and my goal in this paper is to argue its potential for validity."

"The One and Indefinite Dyad were for the Pythagorean Plato the Principles behind all of existence. In the end, I suspect that this was the great Pythagorean secret that Plato could not openly reveal, but only hint at, expecting his attentive followers to abduct the solution. We begin to see why Plato was so careful not to reveal the real nature of the Golden Section and its reciprocal, respectively the Greater and the Lesser."

Alpha- The Fine Structure Constant
â[1/137] is one of the greatest damn mysteries of physics: a magic number that comes to use with no understanding by man. You might say the âhand of Godâ wrote that number, and âwe donât know how He pushed His pencil.ââ âRichard P. Feynman, QED
The fine structure constant is a unit less physical parameter that has the approximate value of 1/137. It is the measure of the strength of the electromagnetic force. It is usually denoted by the lower case Greek letter, alpha. It was first introduced in 1916 by Arnold Sommerfeld (a teacher of Werner Heisenberg) in order to explain the fine structure of energy levels found in the hydrogen atom. The fine structure constant is defined as:

The physical origin of this constant pertains to the closely spaced groups of optical spectrum lines of gases, like hydrogen. Optical spectrum lines are unique in a particular element because they have their own specific energy levels; it is like an elementâs âfinger printâ.
Our understanding of the fine structure constant has evolved since its initial introduction by Sommerfeld. Alpha is now considered to be the coupling constant for the electromagnetic force, just like there are coupling constants for the gravitational force, the weak nuclear force, and the strong nuclear force.
The fine structure constant is quite mysterious and has baffled many physicists, mathematicians and anybody else who has been concerned because there are several bizarre numerical coincidences involving the digits 137. Especially coincidences involving other unit less mathematical constants such as <font color=red>e, pi, and the golden ratio</font>. Here are a few interesting examples of numerical coincidences (note that these are approximate values):

Here is a comical quote from Leon Ledermanâs book The God Particle that pokes fun at Wolfgang Pauliâs obsession with the number 137:
âOne of the wonderful (but unverified) stories in physics emphasizes the importance of 137 as well as illustrating the arrogance of theorists. According to this tale, a notable Austrian mathematical physicist of Swiss persuasion, Wolfgang Pauli, went to heaven, we are assured, and, because of his eminence in physics, was given an audience with God.
âPauli, youâre allowed one question. What do you want to know? Pauli immediate asked the one question that he has labored in vain to answer for the last decade of his life. âWhy is alpha equal to one over one hundred thirty-seven?â
God smiled, picked up the chalk, and began writing equations on the blackboard. After a few minutes, She turned to Pauli, who waved his hand. âDas ist falsch! [Thatâs baloney!]â
This anecdote not only illustrates the arrogance of some theorists as Lederman pointed out, but perhaps how absurd nature may seem to us because it does not always conform to our understanding and what we perceive as reason. Or ironically, God not knowing the answer and Pauli calls Her on it.
Oddly enough, there have been recent discoveries that the fine structure constant, may not be so constant. Visit the following website to find out more: http://focus.aps.org/v8/st9.html